Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Seite 5
... mind , and therefore the simplest applications of its truths are to be found among men of all nations at an early part of their progress towards civilisation . At such a period , doubtless , the minds of men would be too much occupied ...
... mind , and therefore the simplest applications of its truths are to be found among men of all nations at an early part of their progress towards civilisation . At such a period , doubtless , the minds of men would be too much occupied ...
Seite 6
... minds of men should , either by natural or providential circum- stances , be earnestly and steadily directed to its cultivation . Now , in the early ages of the world , human beings were principally urged to vigorous exertions of body or ...
... minds of men should , either by natural or providential circum- stances , be earnestly and steadily directed to its cultivation . Now , in the early ages of the world , human beings were principally urged to vigorous exertions of body or ...
Seite 8
... to be found , and having improved and enriched his mind by the wisdom of their communications , he , on his return , founded a school at Crotona in Italy , where he acquired great renown both as a philosopher and a 8 PREFACE .
... to be found , and having improved and enriched his mind by the wisdom of their communications , he , on his return , founded a school at Crotona in Italy , where he acquired great renown both as a philosopher and a 8 PREFACE .
Seite 11
... minds of his followers a fondness for the study . Finding that their predecessors had nearly exhausted the departments of plane and solid geometry as then known , they looked around for new subjects for the exercise of their talents ...
... minds of his followers a fondness for the study . Finding that their predecessors had nearly exhausted the departments of plane and solid geometry as then known , they looked around for new subjects for the exercise of their talents ...
Seite 21
... mind of the learner is gradually led on from the consideration of the simplest truths to the comprehension of the most recondite theorems . In this respect , the elements may be regarded as an uninterrupted chain of reasonings rather ...
... mind of the learner is gradually led on from the consideration of the simplest truths to the comprehension of the most recondite theorems . In this respect , the elements may be regarded as an uninterrupted chain of reasonings rather ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Keine Leseprobe verfügbar - 2008 |
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AC is equal acute alternate angles ancient angle ACD angle BAC angles ABC appears application assume axiom base BC bisect called centre circle circumference coincide common conclusion construction definition demonstration describe determined diagonal draw drawn elements employed established Euclid extended exterior angle extremities four right angles geometers geometry given point given straight line greater half Hence included angle interior opposite angle intersect introduced join knowledge less Let ABC magnitudes manner means measurement meet method mind mode necessary obtuse parallel lines parallelogram perpendicular plane position principle problem produced proof properties PROPOSITION proved radiant reason rectangle rectilineal figure remaining respects side AB side AC surfaces THEOR theorem thing third triangle ABC triangles are equal truths unequal vertex wherefore whole
Beliebte Passagen
Seite 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Seite 46 - Any two angles of a triangle are together less than two right angles.
Seite 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Seite 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Seite 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Seite 68 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Seite 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Seite 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.